To look for candidate metabolite-methylation pairs, I ran three linear models and selected based on the p value cutoffs below (e.g. metabolite and methylation associated at p < 0.01, and both associated with IA status at p < 0.01).
Using this mediation structure, there were 1490 pairs selected with 58 unique metabolites.
| feature | name |
|---|---|
| gctof_214 | 5930 |
| hilic_32 | Histidine |
| hilic_92 | Unknown |
| hilic_100 | Unknown |
| hilic_113 | Unknown |
| hilic_148 | Unknown |
| hilic_156 | Unknown |
| hilic_174 | Unknown |
| hilic_176 | Unknown |
| hilic_195 | Unknown |
| hilic_200 | Unknown |
| hilic_245 | Unknown |
| hilic_251 | Unknown |
| hilic_271 | Unknown |
| hilic_273 | Unknown |
| hilic_275 | Unknown |
| hilic_307 | Unknown |
| hilic_346 | Unknown |
| hilic_357 | Unknown |
| hilic_368 | Unknown |
| hilic_385 | Unknown |
| hilic_386 | Unknown |
| hilic_387 | Unknown |
| hilic_388 | Unknown |
| hilic_390 | Unknown |
| hilic_391 | Unknown |
| hilic_467 | Unknown |
| hilic_483 | Unknown |
| hilic_528 | Unknown |
| hilic_697 | Unknown |
| hilic_714 | Unknown |
| hilic_724 | Unknown |
| hilic_725 | Unknown |
| hilic_726 | Unknown |
| hilic_750 | Unknown |
| hilic_759 | Unknown |
| hilic_904 | Unknown |
| hilic_996 | Unknown |
| hilic_997 | Unknown |
| lipid_111 | PC (p-32:0) or PC (o-32:1) |
| lipid_143 | PE (38:4) |
| lipid_154 | SM (d34:2) |
| lipid_428 | Unknown |
| lipid_435 | Unknown |
| lipid_445 | Unknown |
| lipid_685 | SM (d34:2) [M+HAc-H]- & [M+Cl]- _YLWSJLLZUHSIEA-CKSUKHGVSA-N |
| lipid_711 | CSH_negESI #569 |
| lipid_719 | CSH_negESI #690 |
| lipid_775 | Unknown |
| lipid_798 | Unknown |
| lipid_801 | Unknown |
| lipid_819 | Unknown |
| lipid_846 | Unknown |
| lipid_855 | Unknown |
| lipid_865 | Unknown |
| lipid_890 | Unknown |
| lipid_992 | Unknown |
| lipid_1111 | Unknown |
Using this mediation structure, there were 600 pairs selected with 23 unique metabolites.
| feature | name |
|---|---|
| hilic_61 | PC(38:4) |
| hilic_345 | Unknown |
| hilic_378 | Unknown |
| hilic_380 | Unknown |
| hilic_397 | Unknown |
| hilic_816 | Unknown |
| hilic_877 | Unknown |
| hilic_975 | Unknown |
| hilic_1012 | Unknown |
| lipid_22 | CE (20:3) |
| lipid_294 | Unknown |
| lipid_329 | Unknown |
| lipid_386 | Unknown |
| lipid_429 | Unknown |
| lipid_494 | Unknown |
| lipid_528 | Unknown |
| lipid_563 | FA (12:0) [M-H]- (lauric acid)_POULHZVOKOAJMA-UHFFFAOYSA-N |
| lipid_568 | FA (16:0) [M-H]- (palmitic acid)_IPCSVZSSVZVIGE-UHFFFAOYSA-N |
| lipid_572 | FA (18:0) [M-H]- (stearic acid)_QIQXTHQIDYTFRH-UHFFFAOYSA-N |
| lipid_856 | Unknown |
| lipid_925 | Unknown |
| lipid_931 | Unknown |
Terms:
\[ Y = \text{IA Status}\\ M = \text{Metabolite at SV}\\ T = \text{Methylation at PSV}\\ X_2 = \text{Sex}\\ X_3 = \text{DR3/4 Status}\\ X_4 = \text{Age at PSV}\\ X_5 = \text{Time from PSV to SV}\\ \text{i indexes subject}\\ \]
\[ M_i = \beta_0 + \beta_1 T_i+\beta_2'C+\epsilon_i\\ \text{With } \epsilon_i\text{ i.i.d. } N(0,\sigma^2) \]
In order to account for the case control design, the mediator model is fit to only the control subjects. The nature of case controls studies means that the cases are over-sampled compared to controls. The regression parameters in the outcome model are consistently estimated in logistic regression, but the study design needs to be taken into account in the mediator model. Fitting this model using only the controls is a good approximation for the regression coefficients that would be obtained in a cohort study, assuming the outcome is rare and that inclusion in the study depends only on the outcome (and not the mediator or exposure).
\[ \text{Let }p=\text{the probability a given subject is an IA case}=P(Y = 1)\\ ln(\frac{p}{1-p}) = \theta_0 +\theta_1 T_i+\theta_2 M_i+\theta_3(T_i*M_i)+\theta_4'C \]
Where \(\beta_2'\) and \(\theta_4'\) are vectors of estimates for multiple confounders \(C\).
CDE is the controlled direct effect. This is how much the outcome would change on average if the mediator was fixed (at m) across the whole population, and the “treatment” (exposure) changed from 0 to 1.
NDE is the natural direct effect. It represents the average change in outcome if the “exposure” changed from 0 to 1, and each individual’s value for the mediator varied as it normally would (in the absence of the exposure). In other words, it is the effect of the exposure on the outcome that would remain if the path from exposure to mediator was removed.
NIE is the natural indirect effect. It is the average change in outcome if the exposure was fixed at 1, but “the mediator were changed from the level it would take if \(t^*=0\) to the level it would take if \(t=1\).” This is essentially the effect of the exposure on the outcome that operates through changing the mediator.
Note, if the interaction term is 0, both the CDE and NDE are equal to the direct effect under Baron and Kenny’s formulation. Also, while CDE, NDE, and NIE are interpreted on the odds scale, proportion mediated is interpreted on the risk scale.
\[ OR^{CDE}(m)=exp(\theta_1+\theta_3 m)\\ OR^{NDE}=exp((\theta_1+\theta_3\beta_0+\theta_3\beta_1+\theta_3\beta_2'C+\theta_3\theta_2\sigma^2)+0.5\theta_3^2\sigma^2)\\ OR^{NIE}=exp(\theta_2\beta_1+\theta_3\beta_1)\\ \text{Proportion mediated (PM)}=\frac{OR^{NDE}(OR^{NIE}-1)}{(OR^{NDE}*OR^{NIE}-1)} \]
In the regmedint summary table, “pure natural direct effect (pnde) is what is typically called the natural direct effect (NDE). The total natural indirect effect (tnie) is the corresponding natural indirect effect (NIE).” link
Because proportion mediated is a highly variables measure and is problematic when the NDE and NIE are in opposite directions, it is generally best to use the estimate and confidence interval for the NIE instead (pg. 48).
There are 52 pairs with significant NIE:
| Pair | NIE |
|---|---|
| cg26981432 & hilic_467 | 46046705.625 |
| cg02223028 & hilic_32 | 9448231.479 |
| cg23110027 & lipid_711 | 7881.339 |
| cg18576552 & hilic_697 | 6191.422 |
| cg17350432 & hilic_32 | 4324.847 |
| cg07375207 & hilic_176 | 4169.481 |
| cg16466870 & hilic_996 | 2677.473 |
| cg24328676 & hilic_174 | 1655.612 |
| cg07375207 & hilic_174 | 672.019 |
| cg15740979 & hilic_996 | 603.111 |
| cg07601148 & hilic_996 | 556.959 |
| cg15052330 & hilic_32 | 254.879 |
| cg07601148 & hilic_174 | 243.600 |
| cg21040069 & lipid_1111 | 226.982 |
| cg02647297 & lipid_775 | 144.116 |
| cg07375207 & hilic_32 | 68.407 |
| cg01709543 & lipid_775 | 60.760 |
| cg00390143 & lipid_711 | 30.334 |
| cg07064673 & hilic_32 | 28.068 |
| cg00390143 & lipid_685 | 21.408 |
| cg01604946 & lipid_111 | 18.519 |
| cg09371112 & hilic_174 | 15.768 |
| cg14410733 & lipid_819 | 14.930 |
| cg00390143 & lipid_775 | 9.155 |
| cg14894245 & hilic_904 | 5.735 |
| cg12616177 & hilic_346 | 2.030 |
| cg03130816 & hilic_113 | 1.791 |
| cg27578381 & hilic_251 | 0.797 |
| cg01042202 & hilic_271 | 0.712 |
| cg19083626 & hilic_483 | 0.703 |
| cg19916129 & hilic_467 | 0.693 |
| cg15142694 & hilic_307 | 0.615 |
| cg23120936 & hilic_174 | 0.603 |
| cg16727231 & hilic_271 | 0.595 |
| cg19083626 & hilic_176 | 0.559 |
| cg19916129 & hilic_176 | 0.498 |
| cg08013331 & lipid_890 | 0.424 |
| cg26612794 & hilic_996 | 0.407 |
| cg19939773 & hilic_32 | 0.405 |
| cg20453969 & hilic_176 | 0.381 |
| cg13649728 & hilic_113 | 0.271 |
| cg16362592 & hilic_391 | 0.107 |
| cg00546307 & hilic_271 | 0.096 |
| cg06320277 & hilic_195 | 0.064 |
| cg00546307 & hilic_251 | 0.059 |
| cg04229103 & hilic_346 | 0.002 |
| cg23466054 & hilic_357 | 0.001 |
| cg20176194 & hilic_32 | 0.000 |
| cg27107970 & hilic_245 | 0.000 |
| cg15130211 & hilic_32 | 0.000 |
| cg08882882 & lipid_992 | 0.000 |
| cg24282826 & lipid_711 | 0.000 |
I think that the problem here is the fact that the metabolites and methylation values are on very different scales, so when you’re multiplying the \(\beta\) values they can occasionally blow up.
When the methylation values are also scaled, the NIE value is much more reasonable:
| x | |
|---|---|
| cde | 0.3715006 |
| pnde | 0.9835381 |
| tnie | 0.7118551 |
| tnde | 0.8236703 |
| pnie | 0.8500204 |
| te | 0.7001366 |
Same again for the next pair:
| x | |
|---|---|
| cde | 1.1786950 |
| pnde | 1.5285937 |
| tnie | 0.5709904 |
| tnde | 1.2064693 |
| pnie | 0.7234434 |
| te | 0.8728123 |
| feature | name | |
|---|---|---|
| 318 | hilic_32 | Histidine |
| 399 | hilic_113 | Unknown |
| 460 | hilic_174 | Unknown |
| 462 | hilic_176 | Unknown |
| 481 | hilic_195 | Unknown |
| 531 | hilic_245 | Unknown |
| 537 | hilic_251 | Unknown |
| 557 | hilic_271 | Unknown |
| 593 | hilic_307 | Unknown |
| 632 | hilic_346 | Unknown |
| 643 | hilic_357 | Unknown |
| 677 | hilic_391 | Unknown |
| 753 | hilic_467 | Unknown |
| 769 | hilic_483 | Unknown |
| 983 | hilic_697 | Unknown |
| 1190 | hilic_904 | Unknown |
| 1282 | hilic_996 | Unknown |
| 1429 | lipid_111 | PC (p-32:0) or PC (o-32:1) |
| 2003 | lipid_685 | SM (d34:2) [M+HAc-H]- & [M+Cl]- _YLWSJLLZUHSIEA-CKSUKHGVSA-N |
| 2029 | lipid_711 | CSH_negESI #569 |
| 2093 | lipid_775 | Unknown |
| 2137 | lipid_819 | Unknown |
| 2208 | lipid_890 | Unknown |
| 2310 | lipid_992 | Unknown |
| 2429 | lipid_1111 | Unknown |
| chr | pos | Name | Probe_rs | Relation_to_Island | UCSC_RefGene_Name | |
|---|---|---|---|---|---|---|
| cg00546307 | chr1 | 1946355 | cg00546307 | NA | OpenSea | |
| cg03130816 | chr1 | 39456103 | cg03130816 | rs4422996 | N_Shore | AKIRIN1;AKIRIN1 |
| cg15052330 | chr2 | 72360243 | cg15052330 | NA | OpenSea | CYP26B1 |
| cg06320277 | chr2 | 105980029 | cg06320277 | NA | OpenSea | FHL2;FHL2;FHL2;FHL2 |
| cg04229103 | chr2 | 145090268 | cg04229103 | NA | Island | GTDC1 |
| cg20176194 | chr2 | 220173205 | cg20176194 | NA | Island | PTPRN |
| cg15142694 | chr3 | 48694534 | cg15142694 | NA | Island | CELSR3 |
| cg15130211 | chr3 | 128276056 | cg15130211 | NA | S_Shore | |
| cg17350432 | chr4 | 841569 | cg17350432 | NA | N_Shore | |
| cg13649728 | chr4 | 128651707 | cg13649728 | NA | Island | SLC25A31 |
| cg23110027 | chr4 | 176394153 | cg23110027 | rs77206097 | OpenSea | |
| cg01042202 | chr5 | 140242159 | cg01042202 | NA | Island | PCDHA6;PCDHA2;PCDHA1;PCDHA9;PCDHA7;PCDHA1;PCDHA6;PCDHA5;PCDHA10;PCDHA3;PCDHA4;PCDHA10;PCDHA8 |
| cg01604946 | chr5 | 148398804 | cg01604946 | NA | OpenSea | SH3TC2 |
| cg15740979 | chr5 | 176958383 | cg15740979 | NA | Island | FAM193B;FAM193B |
| cg02647297 | chr6 | 3867369 | cg02647297 | NA | OpenSea | |
| cg24328676 | chr6 | 32134970 | cg24328676 | NA | Island | EGFL8 |
| cg19939773 | chr6 | 32729876 | cg19939773 | NA | Island | HLA-DQB2 |
| cg23120936 | chr6 | 44251344 | cg23120936 | NA | N_Shelf | TCTE1 |
| cg08882882 | chr6 | 84937375 | cg08882882 | NA | Island | KIAA1009 |
| cg16727231 | chr6 | 139485336 | cg16727231 | NA | N_Shelf | HECA |
| cg16362592 | chr7 | 35289568 | cg16362592 | NA | N_Shelf | TBX20;TBX20 |
| cg19083626 | chr7 | 55322087 | cg19083626 | NA | N_Shore | |
| cg01709543 | chr7 | 98592411 | cg01709543 | NA | OpenSea | TRRAP |
| cg12616177 | chr7 | 100434510 | cg12616177 | NA | N_Shore | |
| cg26981432 | chr8 | 23307949 | cg26981432 | NA | OpenSea | ENTPD4;ENTPD4 |
| cg21040069 | chr8 | 145732410 | cg21040069 | rs45592435 | N_Shore | GPT |
| cg20453969 | chr10 | 27541301 | cg20453969 | NA | Island | LOC387646 |
| cg18576552 | chr10 | 44434381 | cg18576552 | NA | OpenSea | |
| cg07064673 | chr11 | 1491308 | cg07064673 | rs62623399 | Island | HCCA2 |
| cg09371112 | chr11 | 12222570 | cg09371112 | NA | OpenSea | MICAL2 |
| cg08013331 | chr12 | 56040208 | cg08013331 | rs77625892 | Island | |
| cg00390143 | chr12 | 132842539 | cg00390143 | NA | Island | GALNT9 |
| cg07601148 | chr13 | 20975917 | cg07601148 | NA | OpenSea | |
| cg19916129 | chr13 | 113242878 | cg19916129 | NA | S_Shore | TUBGCP3 |
| cg16466870 | chr14 | 101926959 | cg16466870 | NA | S_Shore | |
| cg14410733 | chr15 | 39624999 | cg14410733 | NA | OpenSea | |
| cg07375207 | chr16 | 717419 | cg07375207 | NA | N_Shore | RHOT2;WDR90 |
| cg02223028 | chr16 | 30536135 | cg02223028 | NA | Island | ZNF768 |
| cg26612794 | chr16 | 88148745 | cg26612794 | rs79104167 | OpenSea | |
| cg27578381 | chr17 | 76814686 | cg27578381 | NA | OpenSea | USP36 |
| cg27107970 | chr17 | 79520734 | cg27107970 | NA | S_Shore | C17orf70;C17orf70 |
| cg14894245 | chr19 | 1106640 | cg14894245 | NA | N_Shore | GPX4;GPX4;GPX4 |
| cg23466054 | chr19 | 22018892 | cg23466054 | NA | S_Shore | ZNF43;ZNF43 |
| cg24282826 | chr21 | 35288546 | cg24282826 | NA | S_Shore | ATP5O |
There are 2 pairs with significant NIE:
| Pair | NIE |
|---|---|
| cg02050985 & lipid_329 | 275.050 |
| cg21507958 & hilic_397 | 18.454 |
| cg21507958 & hilic_1012 | 12.706 |
| cg26428191 & hilic_1012 | 8.024 |
| cg26378982 & lipid_931 | 3.504 |
| cg10494860 & hilic_1012 | 2.484 |
| cg16469223 & lipid_386 | 2.031 |
| cg24115232 & lipid_563 | 0.542 |
| cg16805215 & lipid_294 | 0.540 |
| cg24998815 & lipid_572 | 0.001 |
| cg24539295 & hilic_1012 | 0.000 |
Same for this structure:
When the methylation values are also scaled, the NIE value is much more reasonable:
| x | |
|---|---|
| cde | 2.3729446 |
| pnde | 2.2986127 |
| tnie | 0.9345334 |
| tnde | 1.9415763 |
| pnie | 1.1063847 |
| te | 2.1481303 |
Next pair:
| x | |
|---|---|
| cde | 3.4546734 |
| pnde | 2.5719766 |
| tnie | 0.9430224 |
| tnde | 2.2068527 |
| pnie | 1.0990455 |
| te | 2.4254316 |
| feature | name | |
|---|---|---|
| 683 | hilic_397 | Unknown |
| 1298 | hilic_1012 | Unknown |
| 1612 | lipid_294 | Unknown |
| 1647 | lipid_329 | Unknown |
| 1704 | lipid_386 | Unknown |
| 1881 | lipid_563 | FA (12:0) [M-H]- (lauric acid)_POULHZVOKOAJMA-UHFFFAOYSA-N |
| 1890 | lipid_572 | FA (18:0) [M-H]- (stearic acid)_QIQXTHQIDYTFRH-UHFFFAOYSA-N |
| 2249 | lipid_931 | Unknown |
| chr | pos | Name | Probe_rs | Relation_to_Island | UCSC_RefGene_Name | |
|---|---|---|---|---|---|---|
| cg26428191 | chr1 | 185380011 | cg26428191 | NA | OpenSea | |
| cg26378982 | chr2 | 11053937 | cg26378982 | NA | Island | KCNF1 |
| cg02050985 | chr2 | 101766314 | cg02050985 | NA | N_Shore | TBC1D8 |
| cg16805215 | chr3 | 137505160 | cg16805215 | NA | OpenSea | |
| cg16469223 | chr3 | 184095245 | cg16469223 | NA | N_Shelf | THPO |
| cg24115232 | chr5 | 1243907 | cg24115232 | NA | Island | SLC6A18 |
| cg24539295 | chr13 | 24462942 | cg24539295 | NA | N_Shore | PCOTH;PCOTH;MIPEP |
| cg24998815 | chr14 | 90798128 | cg24998815 | NA | N_Shore | C14orf102;C14orf102 |
| cg21507958 | chr17 | 78818871 | cg21507958 | NA | S_Shore | RPTOR;RPTOR |
| cg10494860 | chr20 | 62693951 | cg10494860 | NA | Island | TCEA2;TCEA2 |